This only applies to people who are already working in the industry (vs. brand new college recruits).

I was directly contacted by a GS recruiter.

It took them over 6 weeks to complete the interview process and background check!

Here's a breakdown of the steps:

1. You get pre-screened by the recruiter.
2. Your resume gets floated around through several groups for which you might be a fit (and that have a headcount budget to hire you).
3. Any groups that want to interview will let HR know they want to hire you.
4. One or more phone interviews (more, if you are remote and will have to relocate).
5. One or more onsite interviews that will last 2-6 hours (if you have the time).
6. If a manager wants to hire you, then the recruiter comes back and negotiates your salary. There may be some back-and-forth phone calls on this if your salary requirements are higher than they anticipated.
7. Assuming this all works out, then you have to go through the background check. This typically takes at least 4 weeks!
8. Assuming that you haven't decided to go work somewhere in the meantime, you'll get an offer and start date.

For software engineering roles, the questions revolve around how you would approach a problem.

For example, how would you design a REST service API for returning documents that require long processing times from multi-terabyte storage, at request rates of 1/hour versus 1k/second?

Another might be:

What is a microservices architecture, and under what typical circumstances would you want to refactor an existing service architecture into a microservice architecture?